Volume 38 Issue 11

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Highlighted Articles

Xinran Ma, Z. C. Tu, and Shi-Ju Ran
Chin. Phys. Lett., 2021, 38 (11): 110301   PDF ( 740 )   HTML ( 294 )
Kun Luo, Wei Chen, Li Sheng, and D. Y. Xing
Chin. Phys. Lett., 2021, 38 (11): 110302   PDF ( 76 )   HTML ( 38 )
Zhiling Wang, Zenghui Bao, Yukai Wu , Yan Li , Cheng Ma , Tianqi Cai , Yipu Song , Hongyi Zhang, and Luming Duan
Chin. Phys. Lett., 2021, 38 (11): 110303   PDF ( 48 )   HTML ( 35 )
Ziping Ye, Feiyang Zhang, Donglian Xu, and Jianglai Liu
Chin. Phys. Lett., 2021, 38 (11): 111401   PDF ( 103 )   HTML ( 197 )
Jia-Qi Guan, Li Wang, Pengdong Wang, Wei Ren, Shuai Lu, Rong Huang, Fangsen Li, Can-Li Song, Xu-Cun Ma, and Qi-Kun Xue
Chin. Phys. Lett., 2021, 38 (11): 116801   PDF ( 171 )   HTML ( 66 )
Jie Jiang, Liuhua Mu, Yu Qiang, Yizhou Yang, Zhikun Wang, Ruobing Yi, Yinwei Qiu, Liang Chen, Long Yan, and Haiping Fang
Chin. Phys. Lett., 2021, 38 (11): 116802   PDF ( 227 )   HTML ( 139 )
Di Wang, Jihai Yu, Feng Tang, Yuan Li, and Xiangang Wan
Chin. Phys. Lett., 2021, 38 (11): 117101   PDF ( 71 )   HTML ( 29 )
Fan Gao and Yongqing Li
Chin. Phys. Lett., 2021, 38 (11): 117302   PDF ( 87 )   HTML ( 41 )
Jianglong Du, Haolan Tao, Yuxin Chen, Xiaodong Yuan, Cheng Lian, and Honglai Liu
Chin. Phys. Lett., 2021, 38 (11): 118201   PDF ( 120 )   HTML ( 245 )
Fei Xie , Yaxiang Lu, Liquan Chen , and Yong-Sheng Hu
Chin. Phys. Lett., 2021, 38 (11): 118401   PDF ( 50 )   HTML ( 33 )
Yu-Ru Liu, Peng-Ye Wang, Wei Li, and Ping Xie
Chin. Phys. Lett., 2021, 38 (11): 118701   PDF ( 40 )   HTML ( 29 )

Current Issue

GENERAL
Deep Learning Quantum States for Hamiltonian Estimation
Xinran Ma, Z. C. Tu, and Shi-Ju Ran
Chin. Phys. Lett. 2021, 38 (11): 110301 .   DOI: 10.1088/0256-307X/38/11/110301
Abstract   PDF(pc) (6001KB) ( 740 ) PDF(mobile)(6460KB) ( 79 ) HTML ( 294
Human experts cannot efficiently access physical information of a quantum many-body states by simply “reading” its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. We demonstrate that convolutional neural network (CNN) can learn from coefficients of many-body states or reduced density matrices to estimate the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states (or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.
Random-Gate-Voltage Induced Al'tshuler–Aronov–Spivak Effect in Topological Edge States
Kun Luo, Wei Chen, Li Sheng, and D. Y. Xing
Chin. Phys. Lett. 2021, 38 (11): 110302 .   DOI: 10.1088/0256-307X/38/11/110302
Abstract   PDF(pc) (646KB) ( 76 ) PDF(mobile)(1025KB) ( 3 ) HTML ( 38
Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between the topologically trivial and nontrivial phases. Here, we show that helical edge states can be identified by the random-gate-voltage induced $\varPhi_0/2$-period oscillation of the averaged electron return probability in the interferometer constructed by the edge states. The random gate voltage can highlight the $\varPhi_0/2$-period Al'tshuler–Aronov–Spivak oscillation proportional to $\sin^2(2\pi\varPhi/\varPhi_0)$ by quenching the $\varPhi_0$-period Aharonov–Bohm oscillation. It is found that the helical spin texture induced $\pi$ Berry phase is key to such weak antilocalization behavior with zero return probability at $\varPhi=0$. In contrast, the oscillation for the trivial edge states may exhibit either weak localization or antilocalization depending on the strength of the spin-orbit coupling, which has finite return probability at $\varPhi=0$. Our results provide an effective way for the identification of the helical edge states. The predicted signature is stabilized by the time-reversal symmetry so that it is robust against disorder and does not require any fine adjustment of system.
Improved Superconducting Qubit State Readout by Path Interference
Zhiling Wang, Zenghui Bao, Yukai Wu , Yan Li , Cheng Ma , Tianqi Cai , Yipu Song , Hongyi Zhang, and Luming Duan
Chin. Phys. Lett. 2021, 38 (11): 110303 .   DOI: 10.1088/0256-307X/38/11/110303
Abstract   PDF(pc) (1352KB) ( 48 ) PDF(mobile)(2355KB) ( 3 ) HTML ( 35
High fidelity single shot qubit state readout is essential for many quantum information processing protocols. In superconducting quantum circuit, the qubit state is usually determined by detecting the dispersive frequency shift of a microwave cavity from either transmission or reflection. We demonstrate the use of constructive interference between the transmitted and reflected signal to optimize the qubit state readout, with which we find a better resolved state discrimination and an improved qubit readout fidelity. As a simple and convenient approach, our scheme can be combined with other qubit readout methods based on the discrimination of cavity photon states to further improve the qubit state readout.
THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Unambiguously Resolving the Potential Neutrino Magnetic Moment Signal at Large Liquid Scintillator Detectors
Ziping Ye, Feiyang Zhang, Donglian Xu, and Jianglai Liu
Chin. Phys. Lett. 2021, 38 (11): 111401 .   DOI: 10.1088/0256-307X/38/11/111401
Abstract   PDF(pc) (444KB) ( 103 ) PDF(mobile)(557KB) ( 30 ) HTML ( 197
Non-vanishing electromagnetic properties of neutrinos have been predicted by many theories beyond the Standard Model, and an enhanced neutrino magnetic moment can have profound implications for fundamental physics. The XENON1T experiment recently detected an excess of electron recoil events in the 1–7 keV energy range, which can be compatible with solar neutrino magnetic moment interaction at a most probable value of $\mu_{\nu} = 2.1 \times 10^{-11} \mu_{\scriptscriptstyle {\rm B}}$. However, tritium backgrounds or solar axion interaction in this energy window are equally plausible causes. Upcoming multi-tonne noble liquid detectors will test these scenarios more in depth, but will continue to face similar ambiguity. We report a unique capability of future large liquid scintillator detectors to help resolve the potential neutrino magnetic moment scenario. With $O$(100) kton$\cdot$year exposure of liquid scintillator to solar neutrinos, a sensitivity of $\mu_{\nu} < 10^{-11} \mu_{\scriptscriptstyle {\rm B}}$ can be reached at an energy threshold greater than 40 keV, where no tritium or solar axion events but only neutrino magnetic moment signal is still present.
ATOMIC AND MOLECULAR PHYSICS
Effect of Electron Correlation and Breit Interaction on Energies, Oscillator Strengths, and Transition Rates for Low-Lying States of Helium
Qing Liu, Jiguang Li, Jianguo Wang, and Yizhi Qu
Chin. Phys. Lett. 2021, 38 (11): 113101 .   DOI: 10.1088/0256-307X/38/11/113101
Abstract   PDF(pc) (397KB) ( 43 ) PDF(mobile)(514KB) ( 0 ) HTML ( 12
The transition energies, E1 transitional oscillator strengths of the spin-allowed as well as the spin-forbidden and the corresponding transition rates, and complete M1, E2, M2 forbidden transition rates for 1$s^{2}$, 1$s$2$s$, and 1$s2p$ states of He I, are investigated using the multi-configuration Dirac–Hartree–Fock method. In the subsequent relativistic configuration interaction computations, the Breit interaction and the QED effect are considered as perturbation, separately. Our transition energies, oscillator strengths, and transition rates are in good agreement with the experimental and other theoretical results. As a result, the QED effect is not important for helium atoms, however, the effect of the Breit interaction plays a significant role in the transition energies, the oscillator strengths and transition rates.
Ab Initio Study of Single- and Double-Electron Capture Processes in Collisions of He$^{2+}$ Ions and Ne Atoms
Xiao-Xia Wang, Kun Wang, Yi-Geng Peng, Chun-Hua Liu, Ling Liu, Yong Wu, Heinz-Peter Liebermann, Robert J. Buenker, and Yi-Zhi Qu
Chin. Phys. Lett. 2021, 38 (11): 113401 .   DOI: 10.1088/0256-307X/38/11/113401
Abstract   PDF(pc) (688KB) ( 11 ) PDF(mobile)(805KB) ( 1 ) HTML ( 10
The single- and double-electron capture (SEC, DEC) processes of He$^{2+}$ ions colliding with Ne atoms are studied by utilizing the full quantum-mechanical molecular-orbital close-coupling method. Total and state-selective SEC and DEC cross sections are presented in the energy region of 2 eV/u to 20 keV/u. Results show that the dominant reaction channel is Ne$^{+}$(2$s2p^{6}$ $^{2}\!S$) + He$^{+}$(1$s$) in the considered energy region due to strong couplings with the initial state Ne(2$s^{2}2p^{6}$ $^{1}\!S$) + He$^{2+}$ around the internuclear distance of 4.6 a.u. In our calculations, the SEC cross sections decrease initially and then increase whereby, the minimum point is around 0.38 keV/u with the increase of collision energies. After considering the effects of the electron translation factor (ETF), the SEC cross sections are increased by 15%–25% nearby the energy region of keV/u and agree better with the available results. The DEC cross sections are smaller than those of SEC because of the larger energy gaps and no strong couplings with the initial state. Due to the Demkov-type couplings between DEC channel Ne$^{2+}$(2s$^{2}2p^{4}$ $^{1}\!S$) + He(1$s^{2}$) and the dominating SEC channel Ne$^{+}$(2$s2p^{6}$ $^{2}\!S$) + He$^{+}$(1$s$), the DEC cross sections increase with increasing impact energies. Good consistency can also be found between the present DEC and the experimental measurements in the overlapping energy region.
CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES
Ideal Spin Hydrodynamics from the Wigner Function Approach
Hao-Hao Peng, Jun-Jie Zhang, Xin-Li Sheng, and Qun Wang
Chin. Phys. Lett. 2021, 38 (11): 116701 .   DOI: 10.1088/0256-307X/38/11/116701
Abstract   PDF(pc) (650KB) ( 15 ) PDF(mobile)(1420KB) ( 1 ) HTML ( 6
Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Compared with ideal hydrodynamics without spin, additional terms at the first and second orders in the Knudsen number ${Kn}$ and the average spin polarization $\chi_{s}$ have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motion for these parameters are derived by conservation laws at the leading and next-to-leading order ${Kn}$ and $\chi_{s}$.
Honeycomb Lattice in Metal-Rich Chalcogenide Fe$_{2}$Te
Jia-Qi Guan, Li Wang, Pengdong Wang, Wei Ren, Shuai Lu, Rong Huang, Fangsen Li, Can-Li Song, Xu-Cun Ma, and Qi-Kun Xue
Chin. Phys. Lett. 2021, 38 (11): 116801 .   DOI: 10.1088/0256-307X/38/11/116801
Abstract   PDF(pc) (867KB) ( 171 ) PDF(mobile)(962KB) ( 37 ) HTML ( 66
Two-dimensional honeycomb crystals have inspired intense research interest for their novel properties and great potential in electronics and optoelectronics. Here, through molecular beam epitaxy on SrTiO$_{3}$(001), we report successful epitaxial growth of metal-rich chalcogenide Fe$_{2}$Te, a honeycomb-structured film that has no direct bulk analogue, under Te-limited growth conditions. The structural morphology and electronic properties of Fe$_{2}$Te are explored with scanning tunneling microscopy and angle resolved photoemission spectroscopy, which reveal electronic bands cross the Fermi level and nearly flat bands. Moreover, we find a weak interfacial interaction between Fe$_{2}$Te and the underlying substrates, paving a newly developed alternative avenue for honeycomb-based electronic devices.
Unexpected Selective Absorption of Lithium in Thermally Reduced Graphene Oxide Membranes
Jie Jiang, Liuhua Mu, Yu Qiang, Yizhou Yang, Zhikun Wang, Ruobing Yi, Yinwei Qiu, Liang Chen, Long Yan, and Haiping Fang
Chin. Phys. Lett. 2021, 38 (11): 116802 .   DOI: 10.1088/0256-307X/38/11/116802
Abstract   PDF(pc) (1580KB) ( 227 ) PDF(mobile)(1879KB) ( 18 ) HTML ( 139
Lithium plays an increasingly important role in scientific and industrial processes, and it is extremely important to extract lithium from a high Mg$^{2+}$/Li$^{+}$ mass ratio brine or to recover lithium from the leachate of spent lithium-ion batteries. Conventional wisdom shows that Li$^{+}$ with low valence states has a much weaker adsorption (and absorption energy) with graphene than multivalent ions such as Mg$^{2+}$. Here, we show the selective adsorption of Li$^{+}$ in thermally reduced graphene oxide (rGO) membranes over other metal ions such as Mg$^{2+}$, Co$^{2+}$, Mn$^{2+}$, Ni$^{2+}$, or Fe$^{2+}$. Interestingly, the adsorption strength of Li$^{+}$ reaches up to 5 times the adsorption strength of Mg$^{2+}$, and the mass ratio of a mixed Mg$^{2+}$/Li$^{+}$ solution at a very high value of $ 500\!:\!1$ can be effectively reduced to $ 0.7\!:\!1$ within only six experimental treatment cycles, demonstrating the excellent applicability of the rGO membranes in the Mg$^{2+}$/Li$^{+}$ separation. A theoretical analysis indicates that this unexpected selectivity is attributed to the competition between cation–$\pi$ interaction and steric exclusion when hydrated cations enter the confined space of the rGO membranes.
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES
Determination of the Range of Magnetic Interactions from the Relations between Magnon Eigenvalues at High-Symmetry $k$ Points
Di Wang, Jihai Yu, Feng Tang, Yuan Li, and Xiangang Wan
Chin. Phys. Lett. 2021, 38 (11): 117101 .   DOI: 10.1088/0256-307X/38/11/117101
Abstract   PDF(pc) (599KB) ( 71 ) PDF(mobile)(1493KB) ( 11 ) HTML ( 29
Magnetic exchange interactions (MEIs) define networks of coupled magnetic moments and lead to a surprisingly rich variety of their magnetic properties. Typically MEIs can be estimated by fitting experimental results. Unfortunately, how many MEIs need to be included in the fitting process for a material is unclear a priori, which limits the results obtained by these conventional methods. Based on linear spin-wave theory but without performing matrix diagonalization, we show that for a general quadratic spin Hamiltonian, there is a simple relation between the Fourier transform of MEIs and the sum of square of magnon energies (SSME). We further show that according to the real-space distance range within which MEIs are considered relevant, one can obtain the corresponding relationships between SSME in momentum space. By directly utilizing these characteristics and the experimental magnon energies at only a few high-symmetry $k$ points in the Brillouin zone, one can obtain strong constraints about the range of exchange path beyond which MEIs can be safely neglected. Our methodology is also generally applicable for other Hamiltonian with quadratic Fermi or Boson operators.
Enhanced Thermoelectric Properties of Cu$_{x}$Se ($1.75 \le x \le 2.10$) during Phase Transitions
Zhongmou Yue, Kunpeng Zhao, Hongyi Chen, Pengfei Qiu, Lidong Chen, and Xun Shi
Chin. Phys. Lett. 2021, 38 (11): 117201 .   DOI: 10.1088/0256-307X/38/11/117201
Abstract   PDF(pc) (3396KB) ( 14 ) PDF(mobile)(3944KB) ( 3 ) HTML ( 15
Coupling of a phase transition to electron and phonon transports provides extra degree of freedom to improve the thermoelectric performance, while the pertinent experimental and theoretical studies are still rare. Particularly, the impaction of chemical compositions and phase transition characters on the abnormal thermoelectric properties across phase transitions are largely unclear. Herein, by varying the Cu content $x$ from 1.75 to 2.10, we systemically investigate the crystal structural evolution, phase transition features, and especially the thermoelectric properties during the phase transition for Cu$_{x}$Se. It is found that the addition of over-stoichiometry Cu in Cu$_{x}$Se could alter the phase transition characters and suppress the formation of Cu vacancies. The critical scatterings of phonons and electrons during phase transitions strongly enhance the Seebeck coefficient and diminish the thermal conductivity, leading to an ultrahigh dimensionless thermoelectric figure of merit of $\sim $1.38 at 397 K in Cu$_{2.10}$Se. With the decreasing Cu content, the critical electron and phonon scattering behaviors are mitigated, and the corresponding thermoelectric performances are reduced. This work offers inspirations for understanding and tuning the thermoelectric transport properties during phase transitions.
Topological Properties in Strained Monolayer Antimony Iodide
Danwen Yuan, Yuefang Hu, Yanmin Yang, and Wei Zhang
Chin. Phys. Lett. 2021, 38 (11): 117301 .   DOI: 10.1088/0256-307X/38/11/117301
Abstract   PDF(pc) (922KB) ( 26 ) PDF(mobile)(1018KB) ( 0 ) HTML ( 6
Two-dimensional (2D) topological insulators present a special phase of matter manifesting unique electronic properties. Till now, many monolayer binary compounds of Sb element, mainly with a honeycomb lattice, have been reported as 2D topological insulators. However, research of the topological insulating properties of the monolayer Sb compounds with square lattice is still lacking. Here, by means of the first-principles calculations, a monolayer SbI with square lattice is proposed to exhibit the tunable topological properties by applying strain. At different levels of the strain, the monolayer SbI shows two different structural phases: buckled square structure and buckled rectangular structure, exhibiting attracting topological properties. We find that in the buckled rectangular phase, when the strain is greater than 3.78%, the system experiences a topological phase transition from a nontrivial topological insulator to a trivial insulator, and the structure at the transition point actually is a Dirac semimetal possessing two type-I Dirac points. In addition, the system can achieve the maximum global energy gap of 72.5 meV in the topological insulator phase, implying its promising application at room temperature. This study extends the scope of 2D topological physics and provides a platform for exploring the low-dissipation quantum electronics devices.
Influence of Device Geometry on Transport Properties of Topological Insulator Microflakes
Fan Gao and Yongqing Li
Chin. Phys. Lett. 2021, 38 (11): 117302 .   DOI: 10.1088/0256-307X/38/11/117302
Abstract   PDF(pc) (1147KB) ( 87 ) PDF(mobile)(1730KB) ( 8 ) HTML ( 41
In the transport studies of topological insulators, microflakes exfoliated from bulk single crystals are often used because of the convenience in sample preparation and the accessibility to high carrier mobilities. Here, based on finite element analysis, we show that for the non-Hall-bar shaped topological insulator samples, the measured four-point resistances can be substantially modified by the sample geometry, bulk and surface resistivities, and magnetic field. Geometry correction factors must be introduced for accurately converting the four-point resistances to the longitudinal resistivity and Hall resistivity. The magnetic field dependence of inhomogeneous current density distribution can lead to pronounced positive magnetoresistance and nonlinear Hall effect that would not exist in the samples of ideal Hall bar geometry.
CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY
Thermal Management of Air-Cooling Lithium-Ion Battery Pack
Jianglong Du, Haolan Tao, Yuxin Chen, Xiaodong Yuan, Cheng Lian, and Honglai Liu
Chin. Phys. Lett. 2021, 38 (11): 118201 .   DOI: 10.1088/0256-307X/38/11/118201
Abstract   PDF(pc) (2015KB) ( 120 ) PDF(mobile)(2366KB) ( 27 ) HTML ( 245
Lithium-ion battery packs are made by many batteries, and the difficulty in heat transfer can cause many safety issues. It is important to evaluate thermal performance of a battery pack in designing process. Here, a multiscale method combining a pseudo-two-dimensional model of individual battery and three-dimensional computational fluid dynamics is employed to describe heat generation and transfer in a battery pack. The effect of battery arrangement on the thermal performance of battery packs is investigated. We discuss the air-cooling effect of the pack with four battery arrangements which include one square arrangement, one stagger arrangement and two trapezoid arrangements. In addition, the air-cooling strategy is studied by observing temperature distribution of the battery pack. It is found that the square arrangement is the structure with the best air-cooling effect, and the cooling effect is best when the cold air inlet is at the top of the battery pack. We hope that this work can provide theoretical guidance for thermal management of lithium-ion battery packs.
Recent Progress in Presodiation Technique for High-Performance Na-Ion Batteries
Fei Xie , Yaxiang Lu, Liquan Chen , and Yong-Sheng Hu
Chin. Phys. Lett. 2021, 38 (11): 118401 .   DOI: 10.1088/0256-307X/38/11/118401
Abstract   PDF(pc) (1142KB) ( 50 ) PDF(mobile)(1281KB) ( 5 ) HTML ( 33
Na-ion batteries (NIBs) have been attracting growing interests in recent years with the increasing demand of energy storage owing to their dependence on more abundant Na than Li. The exploration of the industrialization of NIBs is also on the march, where some challenges are still limiting its step. For instance, the relatively low initial Coulombic efficiency (ICE) of anode can cause undesired energy density loss in the full cell. In addition to the strategies from the sight of materials design that to improve the capacity and ICE of electrodes, presodiation technique is another important method to efficiently offset the irreversible capacity and enhance the energy density. Meanwhile, the slow release of the extra Na during the cycling is able to improve the cycling stability. In this review, we would like to provide a general insight of presodiation technique for high-performance NIBs. The recent research progress including the principles and strategies of presodiation will be introduced, and some remaining challenges as well as our perspectives will be discussed. This review aims to exhibit the basic knowledge of presodiation to inspire the researchers for future studies.
Acceleration of DNA Replication of Klenow Fragment by Small Resisting Force
Yu-Ru Liu, Peng-Ye Wang, Wei Li, and Ping Xie
Chin. Phys. Lett. 2021, 38 (11): 118701 .   DOI: 10.1088/0256-307X/38/11/118701
Abstract   PDF(pc) (870KB) ( 40 ) PDF(mobile)(966KB) ( 2 ) HTML ( 29
DNA polymerases are an essential class of enzymes or molecular motors that catalyze processive DNA syntheses during DNA replications. A critical issue for DNA polymerases is their molecular mechanism of processive DNA replication. We have proposed a model for chemomechanical coupling of DNA polymerases before, based on which the predicted results have been provided about the dependence of DNA replication velocity upon the external force on Klenow fragment of DNA polymerase I. Here, we performed single molecule measurements of the replication velocity of Klenow fragment under the external force by using magnetic tweezers. The single molecule data verified quantitatively the previous theoretical predictions, which is critical to the chemomechanical coupling mechanism of DNA polymerases. A prominent characteristic for the Klenow fragment is that the replication velocity is independent of the assisting force whereas the velocity increases largely with the increase of the resisting force, attains the maximum velocity at about 3.8 pN and then decreases with the further increase of the resisting force.
16 articles